An approximation of flights, delays and costs for different forecast scenarios: A backcasting exercise

Air Navigation Service Providers (ANSPs) play a critical role as a natural monopoly within the air traffic system and are subject to regulation. Achieving preset performance targets necessitates efficient resource planning, contingent upon accurate traffic forecasts. This means that forecast precision is a key determinant of operational efficiency. In this study, we employ backcasting techniques to gauge the influence of forecast errors on air traffic management performance. This is done for eleven airspaces and seven years of data. The paper seeks to estimate the cost of delays if the actual number of flights for the period 2015–2020 had been as predicted by EUROCONTROL through its specialised service STATFOR. To assess the impact of forecasting errors, we analyse the discrepancy between the predicted and actual figures for flight data, specifically focusing on delays. Our results show that forecast errors have a noteworthy, adverse effect on performance. Inaccurate predictions prevent efficient resource allocation. We prove that a marginal increase in forecast quality would significantly reduce overall costs for stakeholders.


ANSP performance
In 2019, air traffic across the European Civil Aviation Conference (ECAC) network increased to an all-time high of more than 11 Mio.flights.In that same year, huge efforts were made to improve overall network performance, as 2018 had proved to be the worst year of the previous ten for Air Traffic Flow Management (ATFM) delays and flight cancellations, with almost 25.5 million minutes attributed.Flight delays entail costs of millions of Euros for airlines, passengers and Air Navigation Service Providers (ANSPs), so better management of these inefficiencies is needed.Despite the strong impact of the COVID-19 pandemic on air transport, demand is expected to increase in the medium to long term, leading to traffic levels similar to those of 2019.
The main goal of benchmarking is to enhance efficiency.In the light of this industry's market dynamics, benchmarking efforts frequently concentrate on assessing the performance of air navigation services.These services play a critical role in ensuring the safety and seamless management of flight operations.They operate as natural monopolies and fall under political regulation.EURO-CONTROL has established four Key Performance Indicators (KPIs), including "cost-efficiency" and "capacity," along with specific targets such as minimising delays, to monitor performance.
Traffic forecasts play a crucial role in the cost and resource planning of an Air Navigation Service Provider (ANSP).Underestimating traffic can lead to delays, especially in airspace that is already saturated, but overestimating it results in higher unit costs (i. e. € per flight hour) and reduced cost efficiency.In consequence, ANSPs are faced with a trade-off between cost efficiency and capacity.
A previous study [1] has demonstrated that a significant number of ANSPs struggle with mispredictions, which can result in inefficiencies, particularly in terms of underestimating flight volumes, which in turn leads to delays.However, it is important to note that this partial inefficiency cannot be attributed to air traffic control, as it is entirely exogenous to its operations.Therefore, the primary recipients of any potential improvement efforts would be the forecasters.

STATFOR, responsibility, scenarios
EUROCONTROL, 1 the pan-European, civil-military organisation that supports European aviation, produces regular statistics through its specialised service STATFOR. 2 We specifically focus on the 7-year forecasts published every spring and autumn, which involve three scenarios: Baseline, High and Low.The range between the high and low scenarios can be interpreted as a confidence interval, representing the range of possible outcomes.
It is important to note that ANSPs need to plan capacity and costs based on one of these scenarios.If the scenarios are not borne out in reality, cost increases usually result.In particular, in the case of underestimation the probability of delay is very likely to increase, depending on other airspace and traffic characteristics (such as saturation and complexity), and with it the associated costs.[1,2] illustrate that there may be significant deviations between forecast and actual figures, and argue in favour of efforts to improve forecasting quality, especially regarding demand for flights.Despite a wide confidence interval, most forecasts are not borne out in the actual number of flights, i.e. actual flight numbers are higher than the high scenario or lower than the low scenario.These results are confirmed by applying metrics for forecast quality (such as the Mean Absolute Percentage Error (MAPE) score).We show that such deviations may have significant implications for the stakeholders of the air traffic system.
The STATFOR 2014 report forecasted traffic growth at European level of 2.4% for 2015 (baseline scenario 3 ), 2.8% for 2016, 2.3% for 2017, 2.3% for 2018, 2.8% for 2019 and 3.1% for 2020.However, unexpected, unplanned-for demand for flights resulted in substantial delays and thus significant financial costs for ANSPs.Europe's air traffic grew by 4.3% from 2016 to 2017 and by 3.8% from 2017 to 2018.This means that STATFOR's estimates of air traffic were rather low and air traffic authorities required ANSPs to plan accordingly.

Literature review: backcasting method
This study seeks to estimate what the cost of delays would have been if the actual number of flights for 2015 to 2020 had been as forecast by STATFOR, i.e. to analyse what delays and subsequent costs may be caused by low-quality forecasting or, to put it another way, by a negative deviation between forecast and actual traffic.This provides a better understanding of what costs can be attributed to unexpected increases in air traffic.This approach is commonly known as backcasting.It is framed within scenario planning literature [3][4][5][6][7].Forecasting predicts the (unknown) future based on current trends while backcasting analyses the future from the opposite direction.It starts by envisioning desired future conditions and then works backward to identify specific policies and programmes that connect that specified future to the present, rather than extrapolating present methods into the future [8][9][10][11][12][13][14].
This method has been used in the field of transportation for sustainable transport and transport planning [15][16][17][18].It enables alternative scenarios to be studied based on a sound methodological approach.However, to our knowledge, to date there have been no such studies on air transport, 4 so this paper fills that gap and represents a considerable advance in that direction.The scope of the paper is limited to saturated ANSPs underestimating traffic forecasts in Reference Period 2 (RP2), which covers 2015-2019. 5 The paper is organised as follows: Section 2 presents the data used in the study.Section 3 details the methodology and Section 4 sets out the main results.Section 5 deals with the limitations of the method while section 6 concludes and suggests further research.
Please note that we use "number of flights" and "demand" as synonyms.There may be differences between them, but we use this simplification for the sake of illustration.

Operational data
To assess the impact of forecasting errors, we analyse the discrepancy between the predicted and actual figures for flight data, focusing on delays.This involves comparing the delay that would have occurred if the prediction had been accurate with the actual observed delay.To carry out this analysis effectively, we require three essential data points: • Predicted flights, i.e. the number of flights forecast for a given period, as published by STATFOR.
• Actual flights, i.e. the real, observed flights that took place during the same period.These data are obtained from PRU.
• Actual delay, i.e. the actual amount of delay experienced by flights during the specified period, as recorded and measured in terms of time.
We use the STATFOR spring reports 6 as our source for forecast flights.However, these forecasts are country-specific.The performance targets regarding capacity and cost efficiency are ANSP-related, so the forecast data need to be transformed from 'flights per country' into 'flights per ANSP'.We do this by using data from the Performance Review Unit (PRU), which are available on EURO-CONTROL's One Sky portal.These data are used for official performance reports, such as [23].
As shown in Fig. 1, the growth rates (forecast by STATFOR) are applied to the ANSP-related flights (provided by PRU) to calculate the forecast flights per ANSP [24].The resulting figure is compared with the actual numbers of flights (again based on PRU data).For Maastricht Upper Airspace Control (MUAC) we use the average of the growth rates forecast for the countries covered (Germany, the Netherlands and Belgium).
The analysis of delays is based on PRU data with no post-op adjustments [25].The database contains data on flights, delays (in minutes), delay causes and the number of delayed flights.Delay is split into several causes, which makes it possible to filter out delays that are not attributable to ANSPs (e.g.weather).In accordance with the identification letters used by EUROCONTROL, causes are described as "CRSTMP"7 delays.Capacity targets stipulate that the total ATFM delay per flight must not be greater than 0.5 min in pan-European air traffic.However, ANSP-specific targets are lower because most flights use multiple airspaces (see also Section 3).These targets are published by some ANSPs for both the overall delay and the CRSTMP delay.
Once this information was collected, saturated airspaces in Europe were identified by following two criteria: 1) average delay minutes (ADM) of 0.1 min or more per flight; and 2) checking whether a high figure for average delay minutes was caused by extreme data.This analysis was conducted using boxplots to show the scattering of daily delay, including median, mean, quartiles and outliers.A large difference between mean and median and long whiskers (or outlier points) indicate a high degree of scattering and suggest that the ADM figure might be caused by an extreme figure (and not by saturated airspace).Fig. 2 shows the average CRSTMP delay for all ANSPs considered.Those to the left of the dashed line are considered to be saturated.
The methodology for selecting saturated airspaces is subject to debate.It is important to acknowledge that many ANSPs cover a large number of sectors, so the representation of flights and delays may only provide average values.Airspace oversaturation and the accumulation of delays may be concentrated in space and time.However, we consider this approach to be valid for several reasons: firstly, benchmarking is primarily conducted at ANSP level and there are no specific target values at sector level.Secondly, the selection of airspaces for backcasting is based on the inclusion of relevant data.Lastly, data availability is often limited to ANSP level, making it practical to analyse and assess performance at that level.

Costs of delay
The first attempt to calculate the monetary cost of one minute of delay, as incurred by airliners in Europe, was made by the Transport Studies Group at the University of Westminster [26].Delays were measured relative to the last flight plan filed, with average costs of 72 Euros per minute of delay.Successive revisions [27,28] were published which included more aircraft types, a gate-to-gate perspective on delay costs and updates on the average cost of delays.The latest revised cost of one minute of delay is 104 Euros, set by the Performance Review Unit in 2019 [29].
However, average values do not seem to be a good representation of real costs, as not all flights are subject to the same delay (i.e. for the same total amount of delays in a given period of time there may be many flights with very short delays or just a few with very long delays), so it is crucial to determine the distribution of delays in order to fully comprehend how they affect the total cost.
By extending the analysis to ten delay classes with a different cost attributed to each class, we can significantly improve the cost calculations.We also estimate a mathematical function for all these cost ranges, which we then apply to the distribution of delays in an (delays due to network solutions/scenarios used to balance traffic demand and capacity), ATC Staffing (delays due to unplanned staff shortages that reduce expected capacity), ATC Equipment (delays due to the non-availability or degradation of equipment used to provide an ATC service that reduce expected or declared capacity), Airspace Management (delays following changes in airspace/route availability due to small-scale military activity that reduce expected or declared capacity) and Special Events (delays due to major sporting, government or social events that reduce planned, declared or expected capacity).
I. Galarraga et al. attempt to enhance the accuracy of cost calculations8 or costs from a climate perspective due to air management [31].

General approach
Analysing forecasting errors entails applying two complementary approaches, which together provide a comprehensive understanding of the situation.These approaches are executed in three fundamental phases to ensure a thorough examination of the data.
1. Flight Analysis: in the first phase, the analysis focuses on studying actual and planned flight data.This involves comparing the number of flights that were forecast or planned with the actual number of flights during the given period.Examining these data reveals any disparities or deviations between the forecast and observed flight volumes.2. Backcasting Delays: the second phase involves a backcasting exercise specifically applied to delays.Backcasting entails determining how much delay there would have been if the forecasts had been accurate.By comparing this backcasted delay with the actual observed delay, the impact of forecasting errors on delays can be determined.This analysis provides insights into the scale and consequences of these errors as determined in phase 1. 3. Cost Analysis: the third phase focuses on assessing the costs associated with the backcasted delays.By quantifying the financial implications of these delays, a comprehensive understanding of the economic impact of forecasting errors can be obtained.
In the first approach, daily flights are clustered into value ranges.By examining the observations (i.e the number of flights of a specific ANSP on a specific day in the specific cluster), it is possible to estimate the probability of exceeding the performance target.The primary objective is to assess the feasibility of the capacity targets specified and determine what clusters (daily flight movements) may be considered unrealistic.Backcasting and delay cost analyses serve as complementary investigations to further enhance the understanding of the situation.

Approach 1. clustered delay analysis
Performance targets are an essential part of economic regulation 9 in Europe.For capacity, the EU-wide delay target is 0.5 min per flight.However, individual targets per ANSP or Functional Airspace Block (FAB) are lower since most flights are controlled by multiple ANSPs or FABs.These targets are based on performance plans.Thus, in our first step we set out to find the probability of these performance targets being missed depending on the flights.
We expect the probability of performance targets being missed to increase as traffic increases.To calculate these probabilities, we use a methodology that classifies flights into specific value ranges.By using value ranges, we can analyse the link between traffic volume and the likelihood of missing performance targets 10 .To ascertain the likelihood, we examine all days where the demand aligns with the specific cluster and observe how frequently the delay target was exceeded.That number is then checked against the total number of observations within that cluster.To ensure robustness, we shift boundaries and classes to perform sensitivity analyses.The analysis is run for each ANSP separately.
Fig. 3 illustrates the analysis conducted on German DFS, where we calculate both the average delay minutes (ADM) and the probability of the delay per flight exceeding a specific limit for each group (cluster).The example given indicates that if the daily demand exceeds 8500 flights there is a 100% probability of the delay target being exceeded.Even when the daily demand is between 6000 and 6500 flights, more than 50% of flights experience delays that exceed the specified target.Additionally, as daily demand increases the average delay minutes also increase, which is not surprising.It is important to note that this investigation focuses specifically on en-route delay targets.Please note that the extreme value for the "5000-5500 flights" cluster is due to a low number of observations (1).Subsequently, it might be assumed that this day was characterised by a significant external shock.
For the backcasting, we need to 'adjust' demand to the number of flights forecast by STATFOR.This adjustment is made for each day and is based on certain restrictive assumptions: • The reduction in flights is distributed evenly over the year. 11 There is no spatial shift of traffic flows.
• The average delay in minutes is constant for each class (it does not change because it might be seen as a proxy for capacity).
• Note that STATFOR also uses historic city pairs for forecasts and increases them to get overflights.This gives rise to the same restriction as in the forecast.
Adjusting the flights might result in redistributing observations across different clusters.Essentially, this redistribution dilutes the distribution of observations, shifting the number of flights towards alternative value ranges.This trend is illustrated in Fig. 4 for German DFS, where the blue columns depict the actual values and the orange columns the backcasted ones.Given the constant capacity, denoted by the specific ADM of the cluster, we determine the (backcasted) delay by multiplying the number of observations by the average delay minutes.Consequently, if observations (flights per day) move to a lower cluster through backcasting, the overall delay decreases.This occurs because the observations are then multiplied by the (lower) ADM value.Consequently, the corresponding delay curve shifts to the left (see Fig. 5).Once the (backcasted) total delays have been calculated, the total costs and the costs per flight can be determined.
The ADM curve further helps to estimate the functional form of the link between delay and demand.One possibility is a linear increase after an offset, on the basis that there is no delay if flights do not exceed a certain threshold.However, this assumption is debatable, as delays can occur even when traffic is low.We therefore assume that there is an exponential link.
Fig. 6 shows the ADM curve (blue) for aggregated data (European airspace).As discussed above in the context of Fig. 3, observations per group may differ and may have extreme values due to a low number of observations.Subsequently, the ADM curve may have some peaks which are probably due to external shocks but not to operational limitations.These peaks may lead to a bias in calculating the delay and subsequently the corresponding costs.
To prevent this, we apply a mathematical flattening, using the functional form (1): where y = delay, x = number of daily flights, and a and b are parameters for optimisation.In other words, we find the exponential function that best fits the observations (minimal quadratic deviation between observations of blue and orange dots). 12In addition to the functional form, it may be assumed that the flattened curve should not indicate a delay if the actual delay is zero.The orange curve in Fig. 6 shows the result for Europe after the exponential fitting. 13Note that the values on the x-axis represent the mean between the cluster boundaries.What we are doing here is to use an exponential function to better fit the data distribution and compare results with both (a) clustered data and (b) using non clustered data together with an exponential function to explain the functional form.If this procedure is applied to ANSP data, the deviating delay costs can be determined more precisely.As shown in Table 1, the backcasted delay is much lower than the actual delay.However, peaks in the ADM curve lead to some distortions.After the curve is flattened, the delay is slightly greater than the backcasted figure.Assuming €104 per minute of delay [26][27][28][29] gives the overall delay costs.Table 1 shows the average CRSTMP delay minutes per flight and the subsequent average costs per flight.

Approach 2. exponential flattening on non-clustered data
For this second analysis, a different method is proposed: (a) daily flights and delay minutes are used; (b) clustered delay analysis is omitted; and (c) exponential flattening is applied to the non-clustered data.The first approach is highly valid for providing a general approximation, but these three points significantly enhance the accuracy of the estimates.
More specifically, data on backcasted flights from the previous model are used to later relate the actual number of flights to the minutes of actual delay via function (1).Note however that the coefficients estimated are different from those in the previous approach.
Backcasted daily delays (in minutes) (BD) for all ANSPs and years are then estimated and divided by the number of delayed flights to give the backcasted mean delay (in minutes).Backcasted delays are thus explored via a different function for each year following an exponential flattening.An example of coefficients a and b, and of the model as a whole, is shown in Table 2 (results for the other ANSPs are shown in Appendix A).SSE (Sum Squared Error) and RMSE (Root Mean Square Error) are measures of goodness-of-fit.R 2 = 1 − SSE SST , where SST is the sum total of squares, i.e. the squared differences between the observed dependent variable and its mean.This process is applied to the rest of the ANSPs.
Note that in many cases the R-square may be low, for two main reasons: first, there is high volatility in daily data and no clusters.When cluster analysis is used data volatility is ignored by calculating average values.This means that above-average values may be offset by below-average values.However, in clustering a great deal of information is lost and the analysis may be more limited (note that in some ANSPs there are 0 min of delay on many days).In the link between delays and flights one part of the behaviour (i.e. the deterministic part) can be easily predicted and the other (i.e. the stochastic part) cannot.With the existing data, only the deterministic part can be calculated, which means that certain non-predictable information (such as strikes, etc.) is not considered in the analysis.
By contrast, when the actual and backcasted daily delay data are grouped into clusters, the R-square is much higher.However, it   can be shown that working with daily data is much more suitable and enhances the analysis.For example, if the daily data in 2018 for DFS are clustered the R-square is 0.9804, which is greater than that obtained in Approach 1, where no daily data were used.This confirms that it is more appropriate to work with daily data, as it gives a better forecast than when clusters are used directly.We now analyse the costs of delays.In this case we use the information on costs per minute from the study by the University of Westminster [28] rather than the average value of €104.These cost data are given for 10 delay ranges, which basically means that the cost varies significantly with the number of minutes accumulated.For example, when the delay is between 1 and 4 min the cost is €16.12 per minute.That figure rises to €336.94 per minute when the delay is greater than 300 min (See Fig. 7).The use of these cost ranges enables us to significantly increase the quality of our cost estimates.This is done in 2 steps using the data in Table 3 below (see Appendix B).
Step two is to apply these cost functions to the number of minutes of actual and backcasted delays.Table 3 below shows that the cost functions estimated fit the real data closely.
The original cost data refer to the figures for the different ranges from the University of Westminster study, i.e. minutes of delay multiplied by cost per minute, where estimated cost functions refer to the results from applying functions ( 2) and (3).

Results
Results are shown for ten saturated airspaces (DFS, DSNA, ANS CR, Austro Control, Croatia Control, DCAC, NATS, NAV Portugal, Skeyes and Skyguide) plus the Maastricht Upper Area Control Centre (MUAC), which manages the upper airspace (from 24,500 to 66,000 feet) over Belgium, the Netherlands, Luxembourg and the north-west of Germany.

Flights
As shown in Table 4, actual flights (i.e. the number of flights that actually take place each year) were higher than expected.The largest difference recorded is for NAV Portugal and the smallest is for ANSCR.The differences are in the range of 4-8% in most cases.
Differences are increasing over time in most ANSPs and range from 0.17% for Austro Control in 2016 to 17.66% for Nav Portugal in 2019 (see Appendix C).

Delays
Backcasted CRSTMP Delay Minutes are lower than actual CRSTMP Delay Minutes.This makes sense as actual flights exceeded the backcasted figures and, in general, the more flights there are, the more minutes of delay there will be.However, note that the exponential shape of the curve means that the difference in percentage terms between the two delays is greater than for the number of flights (see Table 5), whichever approach is applied (i.e.clustered analysis or non-clustered daily data).That is, the delays increase by proportionally more than the number of flights.In particular, the deviations between actual and backcasted delays exceed 21% for all ANSPs.
The results for each year are shown in Appendix D. I. Galarraga et al.

Cost of delays
Because backcasted delays are lower than actual CRSTMP delays, the cost of delays is also lower.The reasoning is that actual delays are caused mainly by the under-provision of services due to forecasts underestimating flights.This is referred to as "costs due to underestimation".When delays are higher, the cost may also increase due to the distribution of delays.

Table 4
Actual and Backcasted Flights and difference in absolute and percentage terms for period 2015-2019 (Source: own work).

Table 5
Difference between Actual and Backcasted CRSTMP Delay Minutes, in aggregate terms, applying clustered analysis and non-clustered daily data.
I. Galarraga et al.
Table 6 shows aggregate actual and backcasted delay costs for both the clustered analysis (i.e. using a figure of €104 per minute of delay) and the non-clustered daily data (using the mathematical functions).The results for each year are shown in Appendix E. The Non-clustered/Clustered column depicts how representative the cost obtained with the non-clustered daily data is with respect to the clustered analysis.For example, when the functions are used the actual delay cost for DFS is 31.23% of the cost obtained using the average of €104 per minute.This is tantamount to saying that the average of the Actual Cost column overestimates the cost by 68.77%.The same applies to backcasted delay costs, albeit to a lesser extent.This makes perfect sense as there are many delays of a few minutes that are automatically overestimated when the average cost is used instead of the much lower cost given by Refs.[27,28].This is why we argue that the accuracy of estimates increases very significantly when the cost functions and the full distribution of the delays are used, with lower than average costs being assigned for delays of a few minutes and far higher than average costs when delays are longer.
In short, it can be seen that there are greater differences between the clustered analysis and the non-clustered daily data because the former uses the average figure of €104, regardless of whether delays last, for example, 1 min or 70 min.By contrast, the exponential flattening of non-clustered data applies the cost functions.Results show that when mathematical functions are used the cost per minute is approximately 30.37% of the average figure of €104 (see Table 7).Considering that a delay of around 45 min is needed for the average cost per minute of delay to be €104, using the average can be seen as overestimating the cost of delays, given that there are many delayed flights with delays of less than 45 min (i.e.there are many delays of a few minutes that incur very low costs).

Overall results
When the 11 ANSPs and 5-year results are aggregated, it emerges that the low quality of the forecasts results in an additional cost of €1.24 billion (an increase of 154%) under the clustered analysis.When the non-clustered daily data are used, the additional cost is only just over half that figure at €678 million (an increase of 200%).The average cost per minute is also greater, with an increase of 127% (see Table 7).
There are two effects which lead to the different results in the cost of delay of 3.5bn EUR and 676 Mio EUR.First, part of the delay is attributable to traffic forecasts.Some 12.7 Mio minutes are therefore not attributable to ANSPs although they still occur for airspace users.Second, the average cost of delay per minute decreases from €104 to €31 due to shorter delays and greater precision in calculating values.(See Fig. 8).

Limitations of the study
This study has several limitations related to some of the assumptions that had to be made for the analysis describe in pages 9 and 10.These could be discussed and would affect some of the results of this paper, but in any case, the method proposed is still a valid, robust technique for such analyses.
The problems in accessing sectoral data are another caveat worth mentioning in this paper.Opening up access to data sources such as EUROCONTROL could significantly enhance the accuracy of the estimates.

Table 6
Actual and backcasted delay costs for the clustered analysis and the non-clustered daily data.
I. Galarraga et al.

Conclusions
By using backcasting it is possible to estimate the number of additional delays caused as a consequence of low-quality forecasting by STATFOR or, in other words, by negative deviations between forecast and actual traffic.This is mainly because of the underestimation of services that results from the forecast number of flights being lower than the number of flights that finally occur.
In this study we first identify saturated airspaces in Europe and then determine the years in which there has been underestimation.Forecasts are transformed into ANSP-related flights, flights are then clustered into classes and average delay minutes and the probability of delay target mismatch is calculated.This approach gives a rough calculation of the CRSTMP delay induced by forecast bias (the number of flights forecast is lower than the actual number of flights).However, the actual contribution to CRSTMP delay might differ from the figures shown, as the reduction in flights shown is evenly distributed over the days.This means that there is no consideration of seasonal effects and no potential changes in traffic flows are considered.Thus, there is no consideration of spatial effects.
Using the ANSP level for performance assessment entails certain limitations.Delays can occur in specific sectors of the airspace and may vary over time, suggesting that a more granular approach is needed.However, we argue that performance assessment and target setting generally focus on ANSP level.ANSPs also have decision-making power, particularly regarding resource allocation.Data availability is another factor to consider.Currently, publicly available data are aggregated at ANSP or state level, making them easier to access and analyse at those levels.Accessing sector-level data would require collaboration with organisations such as EURO-CONTROL, which possess the necessary data resources.
We therefore also propose an alternative method for estimating these figures comprising three steps: a) econometric estimation of functions (for each ANSP and year) linking the number of flights and delays; b) cost calculation, for which we estimate an econometric (mathematic) function for the costs of delay based on the study by Refs.[27,28]; and c) application of the cost function to estimated delays considering the full distribution of delays, i.e. for every ANSP and year.This makes it possible to significantly increase the accuracy of the estimates and provides lower estimates of the overall costs of delays.
This last method makes two improvements on earlier methods.Eliminating the cluster analysis means that functions linking flights to delays can be better estimated, as daily data are used.Applying the cost function also means that the accuracy of the cost estimates improves very significantly, as the cost range information estimated by Refs.[27,28] is used.
Results show significant increases in delays due to low-quality forecasting, resulting in major financial costs.Likewise, the cost of delay estimated using the non-clustered daily data is significantly lower than that estimated via the clustered analysis.As argued, this is mainly due to increased accuracy of estimation.
From a total financial cost viewpoint, forecast inaccuracies and their consequences need to be taken into account as the attributable costs of delays are significant and may be higher than costs for spare capacity.Unused capacity may therefore still be cost-optimal as it may pay off for airspace users, passengers and the functioning of the network.This is not considered here in terms of reactionary delay.
In the future, it would be useful to explore the possibility of analysing sectoral data using tools such as NEST.This would involve obtaining sector-level data from relevant authorities or organisations.However, it should be noted that accessing and utilising sectorlevel data would require data to be provided by EUROCONTROL or other relevant sources.

Table 1
Delay and Costs for DFS, 2019 (Source: own work).
I.Galarraga et al.

Table 7
Overall results (Source: own work).

Table B1
ATFM delay ranges and weighted costs (average and per minute) in 2010 Euros : own work based on Table J5 in Cook & Tanner (2011).These are 2010 values, but we need 2015 values.Considering that the network average cost of ATFM delay was 100 Euros/minute in 2017 values, as explained above, and 81 Euros/minute in 2010 values, there was an increase of 23.45%.By applying this percentage increase to the figures in the last row of TableB1, an approximation of ATFM delay cost per minute in 2015 values can be calculated.Actual and backcasted CRSTMP delay costs using an average value of €104 per minute and costs due to underestimation Source

Table E2
Actual and backcasted CRSTMP delay costs using the cost functions and costs due to underestimation